We first define the cluster process (CP). Let \(\Phi _\mathrm {p}=\lbrace \mathbf {x}_i,i\in \mathbb {N}\rbrace \)  be a PP where \(\mathbf {x}_i\)  denotes the location of the \(i\) -th point. For each point \(\mathbf {x}_i\) , associate a PP
\(\Phi _{(i),\mathrm {d}}=\lbrace \mathbf {y}_{(i),j}\rbrace \) . The point \(\mathbf {x}_i\)  is termed the parent point and \(\Phi _{(i),\mathrm {d}}\)  is its daughter point process. The first PP, \(\Phi _\mathrm {p}\) , consisting of all parent points is called the parent process [1]}. The union \(\Phi \)  of all daughter PPs centered at their parent points \(\mathbf {x}_i\)  is termed as CP i.e. 
\({-1}\Phi &=\cup _{\mathbf {x}_i\in \Phi _\mathrm {p}}\mathbf {x}_i+\Phi _{(i),\mathrm {d}}\\&=\left\lbrace \mathbf {z}_{ij}:\mathbf {z}_{ij}=\mathbf {x}_i+\mathbf {y}_{(i),j},\mathbf {x}_i\in \Phi _\mathrm {p},\mathbf {y}_{(i),j}\in \Phi _{(i),\mathrm {d}}\ \forall \ \ i,j\right\rbrace .\) 
